A note on topological semigroup-groupoid

Abstract

In this paper we prove that the set of homotopy classes of paths in topological semigroup is a semigroup-groupoid. Further, we define the category TSGCov/X of topological semigroup coverings of X and prove that its equivalent to the category SGpGpdCov/of covering groupoids of the semigroup-groupoid . We also prove that the topological semigroup structure of a topological semigroup-groupoid lifts to a universal topological covering groupoid.